Though the puzzle doesn't mention, one can suppose by the range of values that degree measure is being used. This is verified by doing the actual calculation in degree measure and then in radian measure:
degree measure:
tot=0; first=1;
for a=0:90-2*first
term=1/(cosd(a)*cosd(a+first));
tot=tot+term;
end
tot
cosd(first)/sind(first)^2
cosd(1)/sind(1)^2
The two answers agree:
ans =
3282.63966557478
ans =
3282.63966557478
In radians:
tot=0; first=1;
for a=0:90-2*first
term=1/(cos(a)*cos(a+first));
tot=tot+term;
end
tot
cos(first)/sin(first)^2
cos(1)/sin(1)^2
tot =
2.00342661950588
ans =
0.76305972223263
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Posted by Charlie
on 2023-12-20 11:23:04 |
observation -- probably obvious -- not a proof